Adrian Nita
Leibnitz on subject and individual
substance
Filozofia Nauki 20/2, 57-65
Adrian Nita
Leibniz on Subject and Individual Substance
The problem of the relationship between subject and individual substance has many philosophical aspects. The subject can be seen in its logical dimension, as cor-related with the predicate; in the psychological dimension, as ego; and, in the epis-temological dimension, as something with perceptions and feelings. These are very important aspects, discussed both in the classical secondary literature on Leibniz1
and recent literature,2 but they can not be discussed in a very short paper like this; we
1
Russell, B., A critical exposition of the philosophy of Leibniz, Cambridge, Cambridge Univer-sity Press, 1900; Couturat, L., La logique de Leibniz d’après documents inédits, Paris, Alcan, 1901; Ishiguro, H., Leibniz’s philosophy of logic and language, Gerald Duckworth & Co Ltd, London, 1972; Parkinson, G. H. R., Logic and reality in Leibniz’s metaphysics, Oxford, Clarendon Press, 1965; McRae, R., Leibniz: Perception, apperception and thought, University of Toronto Press, To-ronto, 1976, etc. The abbreviations used in this paper are as follows: A: Leibniz, G. W., Sämtliche
schriften und briefe, Akademie der Wissenschaften zu Berlin, Darmstadt und Berlin, 1923; GP: C. I.
Gerhardt (ed.), Die philosophischen schriften von Leibniz, 7 volumes, Berlin, 1875-1890 (repr. Hil-desheim, Olms, 1960-1961); C: Couturat, L. (ed.), Opuscules et frangments inedits de Leibniz, Pa-ris, 1903 (repr. Hildesheim, Olms, 1961); L: Leibniz, G. W., Philosophical papers and letters, translated by Leroy E. Loemker, second edition, Dordrecht, Reidel, 1969. The paper is a version of my intervention at the IX International Leibniz Congress (Hannover, 2011), published in the Con-gress proceedings. I am indebted to Pauline Phemister for comments and useful suggestions on ear-lier version of the paper. This work was supported by a grant from the Romanian National Authority for Scientific Research, CNCS — UEFISCDI, project number PN-II-ID-PCE-2011-3-0739.
2De Gaudemar, M., Leibniz: De la puissanse au sujet, Paris, Vrin, 1994; Di Bella, S., The science
of individual: Leibniz’s ontology of individual substance, Dordrecht, Springer, 2005; Jolley, N., Leibniz, London, Routledge, 2005; Nita, A., La métaphysique du temps chez Leibniz et Kant, Paris,
L’Harmattan, 2008; Garber, D., Leibniz: Body, substance, monad, New York, Oxford University Press, 2009; Schulthess, D.D., Leibniz et l’invention des phénomènes, Paris, PUF, 2009; Woolhouse, R., Starting with Leibniz, London, Continuum, 2010, etc.
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will focus on the theory of complete concept, with the emphasis on the metaphysical implications of this theory, rather than on the epistemological aspects. Some ques-tions that demand an answer are: Are there two individual substances of the same kind? What is the nature of a substance that is only possible? What kind of notion does the unactualised possible have? What is the nature of the relationship between the individual substance and its complete notion? In order to answer these questions we will present the concept of individual substance in the first part of the paper; in the second part, we will focus on the problem of whether the possible objects have, or have not, a complete concept; and in the third part we will provide some addi-tional arguments to support our answer.
1. In his Discourse on Metaphysics (1686), Leibniz introduces the notion of in-dividual substance in order to “distinguish the actions of God from those of crea-tures”. So, maintains Leibniz, when “a number of predicates are attributed to a single subject while this subject is not attributed to any other, it is called an individual sub-stance”.3 This Aristotelian position, that there is a correspondence between subject
and predicate at the logical level, and between substance and attributes at the onto-logical level, offers solutions to very important philosophical problems. Given that all true predications have a reason in the nature of things,4 there is a distinction
be-tween substance and accident, on the one hand, and complete being and incomplete being, on the other hand. In a broad sense, a substance is a complete being that has a notion so perfect that it suffices to contain all the predicates of the subject. In this sense, the substance appears as an individual substance.
The reference to God in the title of eighth paragraph of the Discourse on
Meta-physics can be understood as follows: God has a perfect knowledge, and a priori, of
all predicates, so he can know all actions of the individual substance, for example, that Alexander the Great will conquer Darius and Porus, and die a natural death or by poison. In comparison, we have an imperfect knowledge, an imperfect concept, so that we can know only through history the predicates of Alexander the Great.
The individual substance expresses the whole universe in its own way, given that included in its concept are all of the experiences belonging to it, together with all of their circumstances, and the entire sequence of exterior events. It is this idea that generated the dispute with Arnauld, in which Leibniz was forced to provide the de-tails of the theory of principles, freedom, compossibility, necessary truth and contin-gent truth, the divine intellect and will, and so on. We will focus on two aspects of
3GP, IV, p. 432; L, p. 307.
4“A: But since there has to be a cause for the truth or falsity of any thought, I ask you where
we shall seek this cause? B: In the nature of things, I think. A: But what if it arises from your own nature? B: Certainly not from my nature alone. For my own nature and the nature of the things of which I think must be such that when I proceed by a valid method I shall necessarily infer the proposition concerned or find it true” (Leibniz, Dialogue on the connection between things and
his demonstration. In his letter of May 1686, Leibniz responds to the allegation that the substances that are only possible are chimeras. Leibniz shows that the possibles do not have reality as actual objects, but they should not be named chimeras given that they have a certain reality, because they exist in the divine intellect. This infinite series of possible beings is associated with an infinity of events and actions of these beings, and God chooses the best series. The importance of the possibles is required just because of the need for this choice. If it was the case that only a series of possi-bles existed, it would lead to the conclusion that God has no place for choice. So, God will be forced to do what he does, and so he will act with an absolute necessity.
Another element of demonstration is that in a true proposition, the predicate (necessary or contingent; past, present or future) is contained in the notion of the subject. In other words, the notion of an individual substance contains not only the series of present or past predicates, but the series of the future predicates. Moreover, the notion of an individual substance expresses everything that takes place in the universe, past, present or future.
Moreover, every substance is like an entire world, and like a mirror of God or of the whole uni-verse which it expresses, each in its own manner, about as the same city is represented differ-ently depending on the different positions from which it is regarded. Thus the universe is in a certain sense multiplies as many times as there are substances, and the glory of God is likewise redoubled by as many wholly different representations of his work. It can even be said that every substance in some way bears the character of God’s infinite wisdom and omnipotence and imitates him as much as it is capable. For it expresses, however confusedly, everything that takes place in the universe, past, present, or future; this resembles somewhat an infinite percep-tion or an infinite knowledge. And since all other substances in their turn express this one in their own way, and adapt themselves to it, it can be said that each extends its power over all the rest in imitation of the omnipotence of the creator.5
We see that the theory of individual substance is the crossing place of very im-portant philosophical themes: possibility, freedom and identity. The individual sub-stance is the tissue of the actual world and also has some relationship with the realm of eternal truth, and so with the possibles. The individual substance is the condition of the possibility for freedom, given that God compares the different series of the world and then can choose the best of all the series.6 Finally, the individual substance
allows a distinction not only between an individual and other individuals, but also between an individual determinate and an individual generic.7
In order that Arnauld cannot draw the conclusion that Leibniz admits a plurality of same individuals, Leibniz has to sustain the argument that the theory of individual substance allows a good understanding of his position, close to that sustained by Thomas Aquinas regarding individuals: that there cannot be two individuals entirely
5
Leibniz, Discourse on Metaphysics 9; L, p. 308.
6See Phemister, P., Leibniz and God’s Freedom to Create, Revue Roumaine de Philosophie,
2007, 51, 1-2, pp. 3-19.
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similar or differing solo numero.8 The explanation is that the individual notion is
complete, in other words, sufficient to distinguish their subjects completely, and so completely different from the concept of a species.
This difference is that the most abstract concepts of species contain only necessary or eternal truths which do not at all depend on the decrees of God (also the Cartesians say they do, you yourself do not seem to be concerned about this point). But the concepts of individual sub-stances, which are complete and suffice to distinguish their subjects completely, and which con-sequently enclose contingent truth or truths of fact, and individual circumstances of time, place etc., must also enclose in their concept taken as possible, the free decrees of God, also viewed as possible, because these free decrees are the principal sources of existences or facts. Essences, on the other hand, are in the divine understanding prior to any consideration of the will.9 The proposition is that in every true affirmative proposition, whether necessary or contingent, universal or particular, the notion of the predicate is in some way in-cluded in that of the subject, praedicatum inest subjecto.10 It is not without
signifi-cance that Leibniz maintains this very important idea in his On freedom (from 1679):
Having thus recognized the contingency of things, I raise the further question of a clear concept of truth, for I had a reasonable hope of throwing some light from this upon the problem of dis-tinguishing necessary from contingent truths. For I saw that in every true affirmative proposi-tion, whether universal or singular, necessary or contingent, the predicate inheres in the subject or that the concept of the predicate is in some way involved in the concept of subject.11
8To Arnauld, 14 July 1686; L, pp. 335-336. See also: “It follows also that there cannot be two
individual things in nature which differ only numerically. For surely it must be possible to give a
reason why they are different, and this must be sought in some differences within themselves. Thus the observation of Thomas Aquinas about separate intelligences, which he declared never differ in number alone, must be applied to other things also. Never are two eggs, two leaves, or two blades of grass in a garden to be found exactly similar to each other. So perfect similarity occurs only in in-complete and abstract concepts, where matters are conceived, not in their totality but according to a certain single viewpoint, as when we consider only figures and neglect the figured matter’’ (Leibniz,
First truths, L 268). ‘‘I own that if two things perfectly indiscernible from each other did exist they
would be two, but that supposition is false and contrary to the grand principle of reason. The vulgar philosophers were mistaken when they believed that there are two things different solo numero, or only because they are two, and from this error have arisen their perplexities about what they called the principle of individuation” (Leibniz to Clarke 5, p. 26; L, p. 700).
9Ibidem; L, p. 332.
10Ibidem; L, p. 337. See also: “It follows further that there are no purely extrinsic
denomina-tions which have no basis at all in the denominated thing itself. For the concept of the denominated
subject necessarily involves the concept of the predicate. Likewise, whenever the denomination of a thing is changed, some variation has to occur in the thing itself. The complete or perfect concept of
an individual substance involves all its predicates, past, present, and future. For certainly it is
al-ready true now that a future predicate will be a predicate in the future, and so it is contained in the concept of the thing” (Leibniz, First truths; L, p. 268).
This very important idea comes after Leibniz’s reflection on the relationship between the propositions. For instance, in his writings on the logical calculus, Leib-niz introduces a distinction between the relationship between subject and predicate in the affirmative proposition, on the one hand, and between the universal proposition and the particular proposition, on the other hand.
Every true categorical proposition, affirmative and universal, signifies nothing but a certain connection between the predicate and the subject — in the direct case, that is, of which I am always speaking here. This connection is such that the predicate is said to be in the subject, or to be contained in it, and this either absolutely and viewed in itself, or in some particular case. Or in the same way, the subject is said to contain the predicate; that is, the concept of the sub-ject, either in itself or with some addition, involves the concept of the predicate. And therefore the subject and predicate are mutually related to each other either as whole and part, or as whole and coinciding whole, or as part to whole.12
When compared, the negative propositions “merely contradict affirmative ones and assert that they are false. Thus a particular negative proposition does nothing but deny that there is an affirmative universal proposition.”13 Finally, in the particular
affirmative proposition it is not necessary for the predicate to be contained in the subject “per se and viewed absolutely, or for the concept of the subject per se to contain the concept of the predicate. It suffices that the predicate be contained in some species of the subject or that the concept of some instances or species of the subject contain the concept of the predicate; of what kind the species must be, the proposition need not express.”14
2. In order to understand the nature of the substance only possible, if it has or has not a complete concept, we have to remember the story of Sextus, from the last para-graphs of the Essays on theodicy.15 Sextus went to Rome, he caused disturbances,
was condemned as a traitor and banished from his country. In the Palais des
desti-nées, Leibniz imagines many worlds that differ from the actual world by at least one
element, so that we can see a set of Sextus: in one world we find a Sextus who is happy and superior, and in another world a Sextus who is satisfied with a modest condition; there is a Sextus of all kinds and in a infinity of ways.
This story of Sextus shows that between the Sextus from the real world (let’s note this with S1) and the Sextus that comes from a city like Corinth (let’s note this
with S2) there are some common predicates and some others that are different. This
S2 homologue or counterpart of Sextus has the first predicates in common with S1
(that is, he is the son of Lucius Tarquinius Superbus, born in the year, and so on), but he differs by the predicates after the decision to obey the oracle (to go to a town like Corinth, to buy a garden, to became rich and beloved, and so on).
12
C, p. 50; L, p. 236.
13Ibidem; L, p. 237. 14L, p. 239.
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Is this notion of S2 incomplete?16 To humans, as limited beings, the notion is
in-complete, given that we cannot accede to all the predicates from this notion, but to an infinite being, things are different. God can see all the predicates, and in a way com-pletely a priori, so he can compare the quantity of good from the world in which S2
lives in order to have a reason for his choice of the existent world.17
It is obvious that the set of predicates from the notion of S1 is different from the
set of predicates of S2, and so Leibniz can say that, concerning all Sextuses, there is
an infinite series of very similar Sextuses, that is Sextuses of every kind and in infi-nite ways.18
Given that the notion of the possible Sextus is complete only from the perspec-tive of God and incomplete from the perspecperspec-tive of created substances, the difference between the two kinds of notions does not depend on the nature of the individual. For God, both an actual individual and a possible individual have a complete notion given that the possibles depend on the divine understanding and do not depend on the will of God. To God, there is no difference in the degree of completeness be-tween Sextus that goes to Rome and Sextus that goes to a town like Corinth.
There is, of course, an objection to this. If Leibniz insists that the notion of a possible individual is complete, how can he distinguish one individual from another? Are there for Leibniz more individual substances or more complete notions of one and the same individual? We appreciate that the story from the last paragraphs of
Theodicy can offer a good insight into the answer. The Sextus from the actual world
has a list of predicates (L1), the Sextus that goes to a town like Corinth has another
list (L2), and the Sextus that goes to Thrace has another list (L3), and so on. In each
of these situations we have a certain individual, that is a subject that contains all his predicates. This is what Leibniz called, in his correspondence with Arnauld,
ratio-nem generalitatis ad individuum.19 Furthermore, it is obvious that Leibniz conceives
16Mc Rae, for example, sustains this position (op. cit., p. 89).
17“Therefore there is contained in the perfect individual concept of Peter or Judas, considered as
merely possible concepts and setting aside the divine decree to create them, everything that will happen to them, whether necessarily or freely. And all this is known by God. Thus it is obvious that God elects from an infinity of possible individuals those whom judges best suited to the supreme and secret ends of his wisdom. In an exact sense, he does not decree that Paul should sin or Judas be damned but only that, in preference to other possible individuals, Peter, who will sin — certainly, indeed, yet not necessarily but freely — and Judas, who will suffer damnation — under the same consideration — shall come into existence, or that the possible concept shall become actual. And although the future salvation of Peter is contained in his eternal possible notion, yet this is not with-out the help of grace, for in the same perfect notion of this possible Peter, there are contained as possibilities the help of the divine grace to be granted to him (Leibniz, First truths; L, pp. 268-269).
18Leibniz, Essay on Theodicy, paragraph 414. 19
“But when I speak of several Adams, I do not take Adam for a determined individual but for some person conceived in a relation of generality (sub ratione generalitatis), under circumstances which seem to us to determine Adam to be an individual but which do not truly do so sufficiently; as for instance when we mean by Adam the first man, whom God puts in a pleasure garden, which he
also a generic Sextus, that is a complete notion in general, sub ratione generalitatis.20
This last generic notion contains all the predicates that there are in the list of predi-cates of all Sextuses. This distinction is the grounds for us to say that Leibniz sus-tains one and only one complete concept of the subject named “Sextus”, and so that there is one and only one individual substance named “Sextus”.21
Concerning the relationship between the subject and the individual substance, we have to understand another important aspect: given that Leibniz sustains that the na-ture of individual substance or complete being has a concept so complete that is suf-ficient to make us understand and deduce from it all the predicates of the subject to which the concept is attributed,22 one can deduce that there is an equivalence
be-tween what is an individual substance and what has a complete concept.23 Such
equivalence is unlikely, given that we have already seen that there are possible be-ings with a complete concept, but who it is very difficult to name “individual sub-stances”. Leibniz said that an individual substance is a “complete being”. Sextus that goes to Corinth is a possible individual that has a complete concept in the following conditions: 1) it is so only for God; and 2) it is so in his world. So, Sextus that goes to Rome is not missing the existence (given that, to Leibniz, the existence is not a predicate that makes the difference between an individual from the actual world and
leaves through sin, and from whose side God makes a woman. But all this does not sufficiently de-termine him, and so there might be several other disjunctively possible Adams, or several individu-als whom these conditions fit. This is true no matter what finite number of predicates incapable of determining all the rest one takes. But that concept which determines a certain Adam must include, absolutely, all his predicates, and it is this complete concept which determines the relation of gene-rality is such a way to reach an individual (rationem generalitatis ad individuum). For the rest, so far removed am I from holding that a single individual is a plurality that I am even deeply convinced of the teaching of St. Thomas about intelligences but hold it is valid generally, namely, that there cannot be two individuals entirely similar or differing only in number’’ (To De Volder, July 14, 1686; L, p. 335).
20Ibidem.
21For a different point of view, see Roger Woolhouse: “An individual substance or complete
being is not just, superficially, a subject of predicates. It is, more deeply, something which has a complete notion or concept which contains all the predicates of which it is the subject. We need to look more closely at this idea that a substance is something with ‘a complete concept’. We might note, first, that Leibniz spoke not only of individual substances as having complete concepts, but also of them as complete beings. This second characterisation is in fact the more basic of the two. It is only because individual substances are complete beings that they have complete concepts” (Roger Woolhouse, op. cit., p. 24). Note that the notion of an individual substance contains not all, but all
consistent predicates of which it is the subject. So, Sextus2 is not a complete being (he is a possible
being), but he has a complete concept.
22Leibniz, Discourse on Metaphysics VIII; L, p. 307. 23
It is Parkinson that sustains a such position: ‘‘He [Leibniz] has said (§ 5.1, pp. 125-126) that every substance has a complete concept and that everything which has a complete concept is a sub-stance; this means that the terms ‘being a substance’ and ‘having a complete concept’ are equiva-lent’’ (Parkinson, op. cit., p. 130, note 3).
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an individual from a possible world24), but he does lack the completeness. This lack
is not determined by the notional aspects, given that a possible individual has a com-plete concept, but with respect to his nature. It is obvious that from God’s point of view there is no difference between Sextus that goes to Rome and Sextus that goes to a town like Corinth.25 The difference depends on God’s will, because the perfect
be-ing wants to brbe-ing into existence Sextus that goes to Rome, but not Sextus that goes to a town like Corinth.
3. The idea of non-equivalence between what is an individual substance and what has a complete concept can be sustained also by the following two arguments. Leibniz does not maintain that an individual substance is a simple list of predicates26
(as it is the case at the logico-linguistic level), but something more profound. At a higher level (the metaphysical level), the individual substance is a moral subject, that is an entity that can be a subject of recompense or punishment; or, it is obvious that the problem of recompense or punishment for Sextus that goes to Corinth is a prob-lem that is not correctly placed. God introduces this aspect only after a comparison between the quantity of good from the world in which there is such a possible indi-vidual with the quantity of good from other worlds. So, only for the indiindi-vidual sub-stance, that is for Sextus that goes to Rome, does the problem of doing good things or bad things arise and only then is it a subject of recompense or punishment.
The second argument is from the substantiality, given that a possible individual lacks a substantial form that gives him unity, individuality and activity. Probably, the best way we can see this aspect is a diachronic view. Understanding the individual substance on the basis of the complete concept is a mark of Leibniz’s middle years,27
when Leibniz needs an element on which to ground his idea of internal changes. The fact that between every two substances there is no causal interaction, leads to the idea that the change depends on internal principles. Translated into logico-linguistic terms, this important metaphysical idea sustains the argument that the individual concept commands all substantial changes and that in the list of the predicates it will not find the relational predicates. The change of emphasis in the years of the 1690s is obvious in A New System of the nature and the communication of substances (1695). Leibniz proposes a new system concerning the nature of the substances even though he declares, from the beginning, that he conceived this system some years before, more precisely in the middle of the 1680s. Without naming them, he refers to Ar-nauld and the Landgrave of Hessen-Rheinfels, with whom he corresponded with
24See also, Gaudemar, op. cit., p. 42.
25Lærke, M., Contingency, Necessity, and the Being of Possibility. Leibniz’s Modal Ontology in
Relation to His Refutation of Spinoza, Revue Roumaine de Philosophie, 2007, 51, 1-2, p. 57.
26For how this is sustained by Russell, op. cit., Ch. 21, p. 50.
27See Rutherford, D., Leibniz and the rational order of nature, Cambridge, Cambridge
spect to his Discourse on metaphysics (1684).28 The initial accent on continuity
(referring to the system) is replaced by an accent on the elements of discontinuity in respect of the substance. Reality, unity and activity only have the “true unities”, that is the formal atoms from which all things are made. The rehabilitation of substantial forms, the nature of which consists in force, sustains the idea that “the forms which constitute substances have been created with the world and that they will subsist al-ways”.29 In these circumstances, the change of the substances is not on the basis of
the complete concept, even if it is caused by an internal principle.
It is only atoms of substance, that is to say, real unities that are absolutely destitute of parts, which are the sources of action and the absolute first principles out of which things are com-pounded, and as it were, the ultimate elements in the analysis of substance. One could call them
metaphysical points. They have something vital, and a kind of perception, and mathematical points are the points of view from which they express the universe. But when a corporeal
sub-stance is contracted, all its organs together make only one physical point with respect to us. Physical points are thus indivisible in appearance only, while mathematical points are exact but are nothing but modalities. It is only metaphysical points, or points of substance, constituted by forms or souls, which are exact and real, and without them there would be nothing real, since there could be no multitude without true unities.30
Finally, in the correspondence with de Volder (1699-1706) Leibniz shows that the change results from the fundamental attribute of the substance, that is the force, given that extended things have unity only in abstract.31 Given that the movement, and the
change in general, results from the derivative forces, the passage from one state to an-other is sustained by this internal principle that is the very law of the series: the present state tends naturally to the next state. In the Monadology, this idea will take the form of the appetition.32 However, even if it plays a small part,33 the theory of the complete
concept is not aborted (but, it will be metamorphosed), given that the singular things have a complete concept and this is what will command the changes.34
28“It is some years ago that I conceived this system and began communicating with learned men
about it, especially with one of the greatest theologians and philosophers of our time, who had been told about certain of my opinions by a person of the highest notability and had found them very paradoxical. After receiving my explanations, however, he retracted in the most generous and edi-fying way possible, and after approving a part of my propositions, he withheld his censure of the others upon which he still did not agree with me” (Leibniz, A New System of the Nature and the
Communication of Substances, as well as the Union between the Soul and the Body 1; L, p. 453).
29Ibidem, 4; L, p. 454. 30Ibidem, 11; L, pp. 456-457.
31To De Volder, 24 March/3 April 1699; L, p. 516.
32“The action of the internal principle which brings about change or the passage from one
per-ception to another can be called appetition. It is true that appetite need not always fully attain the whole perception to which it tends, but it always attains some of it and reaches new perceptions” (Leibniz, Monadology 15; L, pp. 644).
33See also, Garber, op. cit., pp. 198-199.
